qspec.normal_chi2_convolved_vx_pdf  (  vx ,  m ,  t ,  scale_e ,  e0 = 0 ,  relativistic = True  )[source]

The probability density at the velocity $v_x$ of particles with kinetic energy $E_x$, distributed according to a convolution of a normal and a $\chi^2_1$ distribution $$\begin{aligned} \rho^\prime(v_x) = m|v_x|\gamma^3(v_x)\rho(E_x(v_x)), \qquad\int\limits_0^\infty \rho^\prime(v_x)\mathrm{d}v_x = 1, \end{aligned}$$ where $\gamma$ is the time-dilation factor and $\rho$ is the probability density function normal_chi2_convolved_ex_pdf.

Parameters:

vxarray_like

The velocity quantiles $v_x$ (m/s).

marray_like

The mass $m$ of the particle (u).

tarray_like

The temperature $T$ of the environment (K).

scale_earray_like

The standard deviation $\sigma_{E_x}$ of the normal distribution (eV).

e0array_like

The mean energy $E_0$ of the normal distribution (eV).

relativisticbool

Kinetic energies are calculated either relativistically (True) or classically (False).

Returns:

rho_vxndarray

The probability density in thermal equilibrium at the velocity vx (s/m).